A level set method for dislocation dynamics

We propose a three-dimensional level set method for dislocation dynamics in which the dislocation lines are represented in three dimensions by the intersection of the zero levels of two level set functions. Since the level set method does not discretize nor directly track individual dislocation line segments, it easily handles topological changes occurring in the microstructure. The dislocation dynamics are not limited to glide along a slip plane, but also account for three-dimensional aspects of their motion: cross-slip occurs naturally and climb is included by fixing the relative climb and glide mobility. The level set dislocation dynamics method was implemented using an accurate finite difference scheme on a uniform grid. To demonstrate the versatility, utility and simplicity of this new model, we present examples including the motion of dislocation loops under applied and self-stresses (including glide, cross-slip and climb), intersections of dislocation lines, operation of Frank-Read sources and dislocations bypassing particles.